This paper will introduce the topic of dynamical systems with both discrete and continuous time variables. Fixed points will be discussed, along with their properties such as stability or topological type. The paper will continue on to define the concept of hyperbolicity and its relevance in determining the structural stability of the system. It will conclude with a definition of a bifurcation ...

We consider the problem of transferring some a priori knowledge in the context of supervised metric learning approaches. While this setting has been successfully applied in some empirical contexts, no theoretical evidence exists to justify this approach. In this paper, we provide a theoretical justification based on the notion of algorithmic stability adapted to the regularized metric learning ...

In order for a patient to be discharged from a hospital unit, a physician must first perform a physical examination and review the pertinent medical information to determine that the patient is stable enough to be transferred to a lower level of care or be discharged home. Requiring an inspection of a patient’s ‘readiness for discharge’ introduces an interesting dynamic where patients may occup...

Stability is often the goal for clearinghouses in matching markets, such as those matching residents to hospitals, students to schools, etc. Stable outcomes absent transfers need not be utilitarian effi cient, suggesting the potential value of transfers. We study the wedge between stability and effi ciency in large one-to-one matching markets. We show stable matchings are effi cient asymptotica...

Network flow games model domains where a commodity can flow through a network controlled by selfish agents. Threshold Network Flow Games (TNFGs) are a form of such games where an agent coalition wins if it manages to send a flow exceeding a certain threshold between a source and a target vertex. Cooperative game theory predicts the agents’ actions in such settings with solutions such as the cor...

We provide partial Lyapunov characterizations for a recently proposed generalization of input-to-state and integral input-to-state stability (ISS and iISS, respectively). This generalization relies on the notion of stability with respect to two measures originally introduced by Movchan [1960]. We show that the two classical Lyapunov characterizations of ISS-type properties, i.e., decrease condi...

In multiagent domains, agents form coalitions to perform tasks. The usual models of cooperative game theory assume that the desired outcome is either the grand coalition or a coalition structure that consists of disjoint coalitions (i.e., a partition of the set of agents). However, in practice an agent may be involved in executing more than one task, and distributing his resources between sever...

— Single server queues with repeated attempts are useful in the modeling of computer and télécommunication Systems. In addition, we consider in this paper the possibility of disasters. When a disaster occurs, all the customers present in the system are destroyed immediately. Using a regenerative approach, we dérive a numerically stable recursion scheme for the state probabilities. This model ca...

In this paper we apply the homotopy analysis method (HAM) to study the van der Pol equation with a linear delayed feedback. The paper focuses on the calculation of periodic solutions and associated bifurcations, Hopf, double Hopf, Neimark-Sacker, etc. In particular we discuss the behavior of the systems in the neighborhoods of double Hopf points. We demonstrate the applicability of HAM to the a...

Anisotropically refined mixed finite elements are beneficial for the resolution of local features such as boundary layers. Unfortunately, the stability of the resulting scheme is highly sensitive to the aspect ratio of the elements. Previous analysis revealed that the degeneration arises from a relatively small number of spurious (piecewise constant) pressure modes. The present article is conce...